{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T19:33:46Z","timestamp":1776108826594,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,22]],"date-time":"2020-09-22T00:00:00Z","timestamp":1600732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11772030, 61933002, 11972325"],"award-info":[{"award-number":["11772030, 61933002, 11972325"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Aeronautical Science Foundation of the PR China","award":["2018ZC51030"],"award-info":[{"award-number":["2018ZC51030"]}]},{"name":"the Public Welfare Research Program of Jiaxing","award":["2018AY32041"],"award-info":[{"award-number":["2018AY32041"]}]},{"name":"the Open Foundation of IFET","award":["2019KF1101"],"award-info":[{"award-number":["2019KF1101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Buckling stability of thin films on compliant substrates is universal and essential in stretchable electronics. The dynamic behaviors of this special system are unavoidable when the stretchable electronics are in real applications. In this paper, an analytical model is established to investigate the vibration of post-buckled thin films on a compliant substrate by accounting for the substrate as an elastic foundation. The analytical predictions of natural frequencies and vibration modes of the system are systematically investigated. The results may serve as guidance for the dynamic design of the thin film on compliant substrates to avoid resonance in the noise environment.<\/jats:p>","DOI":"10.3390\/s20185425","type":"journal-article","created":{"date-parts":[[2020,9,22]],"date-time":"2020-09-22T09:40:56Z","timestamp":1600767656000},"page":"5425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Vibration Analysis of Post-Buckled Thin Film on Compliant Substrates"],"prefix":"10.3390","volume":"20","author":[{"given":"Xuanqing","family":"Fan","sequence":"first","affiliation":[{"name":"Institute of Solid Mechanics, Beihang University (BUAA), Beijing 100191, China"}]},{"given":"Yi","family":"Wang","sequence":"additional","affiliation":[{"name":"Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University, Ningbo 315800, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9865-5221","authenticated-orcid":false,"given":"Yuhang","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Beihang University (BUAA), Beijing 100191, China"},{"name":"Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University, Ningbo 315800, China"}]},{"given":"Haoran","family":"Fu","sequence":"additional","affiliation":[{"name":"Frontier Research Center, Institute of Flexible Electronics Technology of THU. Zhejiang, Jiaxing 314006, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1038\/nnano.2017.150","article-title":"Wearable Electronics Nanomesh on-skin electronics","volume":"12","author":"Rogers","year":"2017","journal-title":"Nat. Nanotechnol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.cossms.2015.01.002","article-title":"Mechanics of stretchable batteries and supercapacitors","volume":"19","author":"Zhang","year":"2015","journal-title":"Curr. Opin. Solid State Mater. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.jmps.2016.02.012","article-title":"A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures","volume":"90","author":"Ma","year":"2016","journal-title":"J. Mech. Phys. 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